In much of what we now call the Muslim world, Muslims are fighting Muslims. The conflicts fall into two broad categories: those in which militants battle militants, and those in which militants battle moderates. The outcomes of these conflicts matter.

Syria is the most visible battlefield in these wars. Initially, Bashir al-Assad, satrap of the regime that rules Iran, was challenged by peaceful protesters demanding basic rights and freedoms. He brutalized them. Today, he is in a duel to the death with an opposition increasingly dominated by such al Qaeda-affiliated groups as Jabhat al-Nusra.

When jihadists are slaughtering jihadists, both sides claiming they are “fighting in the way of Allah,” a measure of schadenfreude is probably inevitable among us infidels. But people of conscience should not discount the human cost: 70,000 Syrian men, women, and children killed over the past two years, more than a million refugees, ancient cities reduced to rubble.

The strategic stakes are high: The overthrow of Assad would deal a body blow to the hegemonic ambitions of Iranian supreme leader Ali Khamenei. In Lebanon, Hezbollah’s hold on power would be weakened. Maximizing these opportunities should be a priority for Western policymakers. You can bet that Iranian and Hezbollah commanders are working on ways to minimize the damage.

Though we can’t predict what happens after Assad falls, we can plan for a range of contingencies. A rule of history is that those who are doing the shooting today will call the shots tomorrow. That implies that the Sunni jihadists will be in the strongest position post-Assad. The more — and the sooner — we bolster anti-jihadist Syrians the better.

Across Syria’s eastern border, al-Qaeda in Iraq has been revived. Iranian-linked Shia jihadist groups also are active again. Together, they are rekindling sectarian strife, which, it turns out, was not caused by the presence of Americans and has not been dissipated by the departure of Americans. Nor is the Shia vs. Sunni conflict only a local phenomenon, the result of corralling different groups within European-drawn borders. Wathiq al-Batat, secretary general of the Iraqi branch of (Shia) Hezbollah, recently threatened to wage jihad against the (Sunni) state to the south, or, as al-Batat memorably phrased it, “the infidel, atheist Saudi regime.”

Across the Mediterranean Sea and the Sahara Desert, AQ-affiliated jihadists conquered and ruled much of Mali for ten months. In January, the French — those old colonial masters — drove them out, to the cheers of a local population proud of their history, culture, and traditions, most vividly expressed in Timbuktu’s ancient mosques, shrines, and libraries. All this and more the jihadists had endeavored to destroy. Why? Because they see Africanized Islam as idolatrous, heretical, and, therefore, intolerable. The battle for Mali is not over. Fighting continued over this past weekend.

Another battlefield is in Tunisia. In February, secular opposition leader Chokri Belaid was assassinated by militants. Last week, my colleague Thomas Joscelyn broke the story that Abu Iyad al Tunisi, head of Ansar al Sharia Tunisia — an AQ-linked group that attacked the U.S. embassy in Tunis on September 14, 2012 — has threatened to wage war against Tunisian government officials “until their downfall and their meeting with the dustbin of history.”

The proximate cause: Tunisian prime minister Ali Larayedh dared to criticize Abu Iyan and other Salafi jihadists — Muslims who attempt to live and fight as did the seventh-century followers of the prophet Mohammed — for their “violence and arms trafficking.”

Larayedh belongs to the Ennahda (Renaissance) party, which was inspired by the Muslim Brotherhood. But Joscelyn perceives a split within it: On one side are Islamists, led by the party’s co-founder, Rashid al-Ghannushi, who, though not Salafi jihadis, are by no means unsympathetic to their goals. On the other side are Larayedh and others who at least recognize that al-Qaeda and similar groups offer nothing but endless bloodshed, oppression, and “Salafi vigilantism,” a phenomenon that (another colleague, Daveed Gartenstein-Ross, writes) has already “spread far and wide, affecting a broad spectrum of Tunisian society. . . . One aspect of attempting to control the religious sphere, for Salafi vigilantes, has been targeting Islamic practices regarded as deviant. A Sufi shrine in the small town of Akuda, 85 miles south of Tunis, was set ablaze by Salafis in January — marking the 35th such attack in a seven month period.”

In Pakistan, Muslim-on-Muslim violence has become chronic, including attacks on Ahmadis — Muslims regarded as heretics by, among others, the Pakistani government — as well as on the Shia minority. Most recently, a bomb was set off in a market district of Quetta, killing more than 80 people. The Sunni militant group Lashkar-e-Jhangvi claimed responsibility.

Pakistani novelist Mohsin Hamid recently wrote in the New York Times that at “the heart of Pakistan’s troubles is the celebration of the militant.” That rings true, but he went on to blame Pakistan’s “fraught relationship with India. . . . Militants were cultivated as an equalizer, to make Pakistan safer against a much larger foe.”

Really? Libya has no problem with India or any of its neighbors, yet Libyan government officials, including Prime Minister Ali Zeidan, a former human-rights lawyer and diplomat, have been receiving death threats from militants. Over the weekend one of Zeidan’s aides was kidnapped.

Thousands of Libyans have dared to demonstrate against jihadist groups, in September even storming the headquarters of Ansar al-Shariah, the militia linked to the attack that killed the U.S. ambassador and three other Americans. Some Libyan protesters chanted: “You terrorists, you cowards. Go back to Afghanistan.”

In Egypt there are protests day after day against attempts by President Mohamed Morsi to replace secular authoritarianism with religious authoritarianism. Militant Muslim Brothers have responded with lethal violence. In 2012, the Brotherhood swept student-union elections at Egyptian universities. Last month, by contrast, it was soundly trounced.

That’s encouraging — though without outside support, it is hard to imagine the moderates prevailing over the militants in Egypt or elsewhere. As for the militant vs. militant wars, it would be best if both sides were to lose. But that outcome is unlikely.

— Clifford D. May is president of the Foundation for Defense of Democracies, a policy institute focusing on national security.